Underwater Board Shape

From Jim Michalak's Boat Designs

Aircraft designers have been trying to predict the performance of wings since the very beginning. The Wright brothers not only developed the airplane but made some of the best wind tunnels of their time. And from the very beginning they noticed that long skinny wings usually performed better than short fat ones. And so it is with the underwater board of a sailboat. In its own way it "flies" through the water producing a force that counteracts the side loads produced by a fore-and-aft sail rig.

Designers quickly developed the term "aspect ratio" to measure that feature of a wing. The aspect ratio of an underwater board is AR=2 x B x B / S, where B is the length of the board and S is its area. Figure 1 shows how you measure those elements. (Aero students will note that the above equation is twice the usual given for an aircraft wing which has two tips while an underwater board has but one tip.)

Next, for a board with a symmetrical cross section (so it can function equally on all tacks), the board must go through the water at an "angle of attack" to generate force, as we discussed in the last issue. Figure 2 shows how the situation applies to a close hauled sail boat. The skipper wants to go to on a certain couse but because of the angle of attack required by the board he must head his boat upwind by the angle of attack. So he might think the boat is "slipping" and producing "leeway" equal to the angle of attack. One other important thing to notice here is that any angle of attack of the underwater board must subtract from the angle of attack of the sails. A bad situation. Sort of a double penalty.

Now look at Figure 3. Here is the big message: High aspect ratio boards (deep and skinny) reach their lift coefficients with less angle of attack than do shallow fat boards. The figure is sort of idealized but Marchaj gives examples of tests of different actual boards that agree with the figure.

Low aspect ratio keels can be successful if they have sufficient area to allow them to always operate at a low C. The Micro has I think about 14 square feet of keel, about twice the value I recommended of 4% of the sail area for a deep skinny fin. Large low aspect ratio keels also make for steadier boats. Marchaj points out that they have superior damping which makes for a safer boat in rough going.

As an example, let's use Frolic2 again. Her board has 4.4 square feet of area immersed and it is 3.5 feet deep. So the aspect ratio is 2 x 3.5 x 3.5/ 4.4 = 5.6. Now let's say we wanted to guess at leeway on a close reach in 10 knots wind, and we'll assume she is going 4 knots at the time. Frolic2 has 114 square feet of sail and 10 knots produces about .5 psf on a typical good sail, so that is 57 pounds of sail force. We'll assume that all of that force is counteracted by the board. So the overall pressure on the board is 57/4.4 = 13 psf. Now we need to calculate the value of C for the fin. Remember that the psf on the fin is = 2.86 x V x V x C. Using V = 4 knots, we can solve for C and get C = .28. Now get into the aspect ratio figure, guess where AR = 5.6 might be and it appears that the leeway angle would be about 4 degrees.

Here's an interesting "what if". What if the Frolic2 narrow board were instead mounted like a shallow keel such that it still has 4.4 square feet of area but now has a length of 3.5 feet and a depth of 1.25 feet? Now its aspect ratio = 2 x 1.25 x1.25 / 4.4 = .71. Going into the aspect ratio chart you would see the leeway for this fin would be about 15 degrees under the same situation.

Let's get one step fancier and say we have the original board set up as a centerboard that folds into a similar sized shallow stub keel as shown in Figure 4. This is a pretty common arrangement. Now the two areas will share the side load, but in what proportion? One thing we can say is that they will operate at the same angle. Let's guess that the angle of attack is 4 degrees. Then the deep skinny board is operating at a C of about .3 while the shallow fat board is operating at a C of about .1. They have the same area so the deep skinny board is producing three times the lift of the stub keel! It's doing nearly all the work. And it will continue to do so until the angle of attack reaches about 15 degrees at which point the deep skinny board reaches C max of about 1.2. Then the stub keel is working at a C of about .3 and will continue to be effective until it reaches an angle of maybe 50 degrees. You wouldn't want to sail at a 50 degree leeway angle although there might be times when it would be advantageous. I can't really think of such a situation.

This sort of analysis flies in the face of some designs. As mentioned earlier, the shallow keel can work very well if given enough area. But I've seen designs with "keel runners" or "chine runners" which I think are just small projections off the bottom. Given what we have seen here I don't see how they can work effectively. I've sailed boats with skids and external chines which approach those things but my boats always had leeboards or centerboards too. If you think the skids and chine runners are effective, you need only take one of my boats out, get close hauled, and raise the leeboard or centerboard to see what happens. You'll slide right off! I don't think those shallow keel and chine runners are effective. (I'd really like to try or see a good test on Matt Leyden's Paradox. That boat has chine projections and nothing else. MAIB ran an excellent series about making a Paradox but, after a year now, no completed photos or test results. My own feeling is that everything about Paradox is optomized for downwind sailing, something the designer is expert at. I'm not making fun of him - few of us have the patience and knowledge to do what Matt has done. But I'm not sure if the builders are aware of what Paradox's limitations might be as far as sailing to windward goes. At any rate, it seems to me that Paradox could be given a more weatherly rig pretty easily with an effective pivoting leeboard and a more balanced lug rig.)

Jim Michalak

1998

Part one

Contact info:

michalak@apci.net

Jim Michalak
118 E Randall,
Lebanon, IL 62254, USA